$f(Q,T)$ gravity, its covariant formulation, energy conservation and phase-space analysis

Abstract

In the present article we analyze the matter-geometry coupled $f(Q,T)$ theory of gravity. We offer the fully covariant formulation of the theory, with which we construct the correct energy balance equation and employ it to conduct a dynamical system analysis in a spatially flat Friedmann-Lemaître-Robertson-Walker spacetime. We consider three different functional forms of the $f(Q,T)$ function, specifically, $f(Q,T)=\alpha Q+\beta T$, $f(Q,T)=\alpha Q+\beta T^2$, and $f(Q,T)=Q+\alpha Q^2+\beta T$ . We attempt to investigate the physical capabilities of these models to describe various cosmological epochs. We calculate Friedmann-like equations in each case and introduce some phase space variables to simplify the equations in more concise forms. We observe that the linear model $f(Q,T)=\alpha Q+\beta T$ with $\beta =0$ is completely equivalent to the GR case without cosmological constant $\Lambda$. Further, we find that the model $f(Q,T)=\alpha Q+\beta T^2$ with $\beta \ne 0$ successfully depicts the observed transition from decelerated phase to an accelerated phase of the universe. Lastly, we find that the model $f(Q,T)=Q+\alpha Q^2+\beta T$ with $\alpha \ne 0$ represents an accelerated de-Sitter epoch for the constraints $\beta <-1$ or $\beta \ge 0$.

EPJC accepted version

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Cited by in corpus (4)

• Existence of Wormhole Solutions in $f(Q,T)$ Gravity under Non-commutative Geometries
• Wormhole Geometry and Three-Dimensional Embedding in Extended Symmetric Teleparallel Gravity
• Statistical and Observation Comparison of Weyl-Type $f(Q,T)$ Models with the $\Lambda$CDM Paradigm
• Exploring the Viability of $f(Q,T)$ Gravity: Constraining Parameters with Cosmological Observations